On Test Generation for Transition Faults with Minimized Peak Power Dissipation

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1 30.3 On Test Generation for Transition Faults with Minimized Peak Power Dissipation Wei Li Sudhakar M. Reddy Irith Pomeranz 2 Dept. of ECE School of ECE Univ. of Iowa Purdue University Iowa City, IA West Lafayette, IN USA USA {li00, reddy}@engineering.uiowa.edu pomeranz@ecn.purdue.edu ABSTRACT This paper presents a method of generating tests for transition faults using tests for stuck-at faults such that the peak power is the minimum possible using a given set of tests for stuck-at faults. The proposed method is suitable for use in testing scan designs that employ enhanced scan. The method reduces the peak power consumption in benchmark circuits by 9% on the average with essentially the same test set size and the same fault coverage compared to an earlier method. Categories and subject descriptors B.8. [Performance and Reliability]: Reliability, Testing and Fault-Tolerance General terms Algorithm, Design, Reliability Keywords Power Dissipation, Test Generation, Transition Faults. INTRODUCTION Physical defects that cause the signal propagation delays in circuits to increase can be modeled as delay faults. Two general types of delay fault models, the gate delay fault model [,2] and the path delay fault model [3,4], have been used to model delay defects. The path delay fault model is. Research supported in part by NSF Grant No. CCR and in part by SRC Grant No. 200-TJ Research supported in part by NSF Grant No. CCR and in part by SRC Grant No. 200-TJ-950 Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. DAC 2004, June 7, 2004, San Diego, California, USA Copyright 2004 ACM /04/0006 $5.00. more comprehensive in modeling delay defects, but often difficult to use in practice due to the large number of paths in large circuits. The gate delay fault model is more practical for large circuits. The most commonly used gate delay fault model is the transition fault model []. Under the transition fault model, there are two types of transition faults, slow-to-rise faults and slow-to-fall faults. A test pattern pair <V, V2> is required to detect the transition fault f on line l. Two conditions have to be satisfied by <V, V2> to detect the transition fault. () The initial vector V must set the target node to an initial value 0 for the slow-to-rise fault and to an initial value for the slowto-fall fault. (2) The test vector V2 has to launch the corresponding transition at the target node and also propagate the fault effect to the primary output. Thus, V2 is a test for a s-a-0 (s-a-) fault if the transition fault is the slow-to-rise (slow-to-fall) fault. Many works have been reported on generating and compacting tests for transition faults [3-6]. It is known that power dissipation may be considerably higher in test mode than in the normal system mode [7,8]. During normal operation, typically a relatively small portion of the flip-flops change value in each clock cycle. However while scanning in test vectors as well as during capture cycles, many more flip-flops may change value in each clock cycle, thus causing much higher average and peak power dissipation than in the normal operation mode. This can cause problems both with heat dissipation and with current spikes. Another problem arises when wafer probe testing is done through spring loaded contacts which may not be able to deliver large enough current to meet the peak current requirement of some scan tests. This may cause a chip to fail a test even when it is defect-free, thus reducing the yield. Recently, yield loss due to voltage drops caused by higher peak current during test of an ASIC chip has been reported in [9]. Using tests with reduced peak current requirement will help reduce the possibility of such occurrences. 504

2 Various techniques have been proposed to reduce power dissipation during test. Two examples are [0] and [] that consider standard scan designs. In this paper, we present a power conscious transition fault ATPG scheme based on the work in [6]. Our scheme consists of three phases. First, we use a MinMax Spanning Tree (MMST) [8] algorithm to construct tests for the easyto-detect faults. Second, we compute the minimum peak power dissipation value without compromising transition fault coverage when tests generated from a given stuck-at fault test set are used. Then, we use this minimum value as a constraint to select test pairs for the remaining faults. Finally, in the third phase we use forward-looking fault simulation [3] to compact the test set. The proposed scheme keeps all the advantages noted in [6] and in addition achieves minimum peak power dissipation. Compared to the method in [6], the peak power reduction is 9% on the average and up to 40%. The remainder of the paper is organized as follows. Section 2 gives definitions of terms used in this paper and a brief review of the previous work in [6]. In Section 3 we formulate the problem and give a sketch of the proposed method. Section 4 introduces the MMST based algorithm. In Section 5, we give the method to select tests for the remaining transition faults under the peak power constraint. In Section 6, the test compaction method is discussed. In Section 7 experimental results are presented. Section 8 concludes the paper. 2. PRELIMINARIES AND REVIEW 2. Terminology and background Below we give the definitions for some terms used in this paper. Definition : The weighted switching activity (WSA) of a node is the number of state changes at the node multiplied by (+node fan-out). The in the formula is to include the output capacitance of the driving gate. The WSA of the entire circuit is obtained by summing the WSA of all the nodes in the circuit. WSA is used to represent the power dissipated in a circuit when a two-pattern test is applied. WSA was also used to represent instantaneous power in earlier works []. Instead one can use an actual power calculation, but it requires a large computation time. Definition 2: The peak power is the highest value of power dissipation at any given instant of switching activity caused by test application. In this paper, the highest value of WSA is used as the peak power. 2.2 Test application Transition fault tests can be applied in three different ways: broadside [4], skewed-load [5] and enhanced-scan [6]. In this paper, we only consider enhanced-scan transition fault tests. When enhanced scan is used, scan cells are made up of three latches. During scan-in of a new vector the previously applied vector is stored in the third latches of the scan flipflops, which drive the combinational logic of the circuit under test. For this reason during scan-in no power is dissipated in the combinational logic of the circuit under test. Power is dissipated in the combinational logic only during capture cycles. 2.3 Review of previous work For designs with enhanced scan one can generate tests for transition faults by composing two-pattern tests from tests for stuck-at faults [6,2]. Compared to the conventional test generation and test application methods for transition faults in standard scan designs, this has the following advantages [6]. Higher fault coverage compared to that achievable in standard scan designs. Enhanced scan allows the detection of all the irredundant transition faults whereas standard scan based tests may not detect all the irredundant faults. Low average power dissipation due to the use of enhanced scan cells, since the inputs to the combinational logic are held at a constant value while the new state is scanned in. Reduced storage space. Normally the size of a transition fault test set is four to five times larger than the size of a stuck-at fault test set. Since the transition fault tests are chosen from a stuck-at fault test set, only the stuck-at fault tests need to be stored and the test data volume is significantly reduced. Simplified validation process. Since the stuck-at fault tests have gone through a validation process, the validation process for the transition fault tests is unnecessary. Despite all the advantages above, the peak power during test may exceed that in normal operation since there is no power saving action addressing the capture cycle. 3. PROBLEM FORMULATION A transition fault test set for an enhanced scan design consists of a sequence of primary input vectors and state vectors that are scanned in. For the sake of simplicity of explanation, we assume as in [6] that all the inputs (i.e., primary inputs and state variables) are scanned. For this case, let T s =<t, t 2,, t N > be a sequence of test vectors scanned in and let T c be a test set for stuck-at faults. We assume that all the tests in T c have to be applied in some order. A pair of consecutive vectors of T s constitutes a twopattern test for transition faults. For example <t, t 2 >, <t 2, t 3 >,,<t i, t i+ > form two-pattern tests. If the transition fault tests are formed from tests for stuck-at faults, then each t i is a member of the test set T c for stuck-at faults. In the test 505

3 sequence T s for transition faults, some of the tests in T c may appear more than once. One obtains a two-pattern test <t, t 2 > for say a slow-to-rise fault on circuit line r by using a test, say t, to detect the s-a- fault on line r (note that t sets line r to 0) and a test t 2 that detects the s-a-0 fault on r. Actually, any test in T c that sets r to 0 can be used for t (even if it does not detect a s-a- fault on r) and any test in T c that detects a s-a-0 fault on r can be used for t 2. In order to construct a sequence T s for transition faults from a test set T c such that the maximum WSA for any twopattern test is the minimum possible using the tests in T c, we create a graph G s (V,E), which is a complete graph called the transition graph. In G s there is a node corresponding to each test in T c and the edge (t i, t j ) has weight w ij which is equal to the WSA during the capture cycle when the two-pattern test <t i, t j > is applied. Since the WSA for (t i, t j ) is equal to the WSA for (t j, t i ), G s is an undirected graph with a weight w ij =w ji on the edge between t i and t j. An example given below illustrates the construction of G s and how transition fault tests with minimum WSA can be obtained from G s. Example: Let T c contain four tests {t, t 2, t 3, t 4 }. The corresponding G s is given in Figure. In G s traversing an edge corresponds to a two-pattern test, which also depends on the direction of traversal. For example <t, t 2 > and <t 2, t > are two different two-pattern tests that detect different transition faults. Thus there are twelve different two-pattern tests corresponding to the six edges in G s of Figure. From these tests we need to select a minimal number of tests to detect all the transition faults that can be detected if all twelve tests are applied. In addition, the maximum of the WSAs in the circuit for all the two-pattern tests used should be minimum. A test sequence T s corresponds to traversing the graph G s starting from a node corresponding to the first test in T s. For example, the test sequence T s = <t, t 2, t 3, t 2, t 4 > corresponds to traversing G s starting from t. The twopattern tests obtained from T s are <t, t 2 >, <t 2, t 3 >, <t 3, t 2 > and <t 2, t 4 >. 4 t t3 3 Figure. An example transition graph In the method we propose the test sequence T s is constructed in three phases. In the first phase we construct a sequence T s that includes all the tests in T c at least once and has the property that the maximum value of WSA for any two consecutive tests in T s is minimum. To define T s, we determine a path in G s such that the path includes every node in G s at least once and the largest weight of an edge included in the path is the minimum among all the paths that can be constructed to include each node of G s at least once. It is well known that an algorithm based on Minimum 2 3 t2 t4 Spanning Tree traversal provides a two-approximate solution for a special case of TSP (the Traveling Salesman Problem) called TSP, which requires visiting each node exactly once with minimum cost [7]. The cost in this case is the sum of the weights of the edges in the path used to visit the nodes. In the problem we consider the goal is to visit each node at least once such that the maximum weight of an edge in the selected path is minimum. To obtain such a path we use a MinMax Spanning Tree [8] (defined later in this section) for G s. In the second phase we extend T s as follows. First we simulate the two-pattern tests obtained from T s to drop all the transition faults detected by them. T s is extended into a sequence T s that includes tests to detect yet-undetected transition faults such that the maximum WSA of the tests included in the extended test sequence is again the minimum among all the possible extensions. The extended sequence T s is compacted without increasing the maximum WSA in the third phase to obtain a minimal length test sequence. Definition 3: Given a graph G(V,E), a spanning tree G T is a connected, cycle-free subgraph that includes all the nodes in G. Definition 4: Given a graph G(V,E) with weighted edges, a spanning tree is called a MinMax Spanning Tree (MMST) if the maximum of the weights of the edges in G T is the minimum among all the spanning trees of G. For example, a MMST for the transition graph of Figure is given in Figure 2. In the next three sections we give the details of the proposed method to generate transition fault tests from a given stuck-at fault test set. t t3 2 Figure 2. A MMST for the transition graph of Figure 4. TEST SEQUENCE BASED ON A MMST The first part of the test sequence for transition faults is derived by constructing a MMST for the transition graph of a given stuck-at test set and traversing the graph using the following procedure. Procedure_MMST(G s (V,E)) Given: A transition graph G s (V,E) corresponding to a stuck-at fault test set T c Step : Sort the edges in E by weight into a list E Step 2: Remove from E all the edges whose weight is equal to the maximum edge weight Step 3: Check to see if a spanning tree made up of edges from E exists for the graph. If such a spanning tree exists, go back to Step 2. Otherwise go to Step 4. Step 4: Restore the edges removed in the last execution of Step 2 into E t2 t4 506

4 Step 5: Construct a spanning tree for G s. This is a MMST for the given G s. The method we use to construct a spanning tree is discussed below. Step 6: Find a path based on the spanning tree constructed in Step 5. The method we use to construct the path is discussed below. This path defines the first part T s of the transition fault test sequence. To generate a spanning tree in Step 5 we apply the Depth- First Search (DFS) algorithm to the graph G s. Since G s is connected, the order by which the nodes are visited for the first time defines a spanning tree called the DFS tree [7]. For example, suppose that the graph shown in Figure 3(a) is obtained after Step 4. Let us start the DFS algorithm from t. Suppose that t 2 is visited first. The algorithm then backtracks to t. Suppose that t 3 and t 4 are visited next. Then the spanning tree is the one shown in Figure 3(b). To construct the path in Step 6 we traverse the spanning tree constructed in Step 5 in depth first manner such that a subtree with a lower depth is traversed earlier. For example, in the spanning tree of Figure 3(b) we first traverse the subtree rooted at t 2 as it has fewer levels than the subtree rooted at t 3 which will be traversed later. The traversal of the subtree rooted at t 2 results in the subsequence t t2. Next, we return to t and traverse the subtree rooted at t3. This results in the sequence t t 2 t t 3 t 4. Figure 3. Method to construct depth-first MMST When we traverse the MMST as discussed above, some nodes may be visited more than once. We shortcut a node that has been visited before by using an edge not in the MMST if the weight of the edge does not exceed the maximum weight of the edges in the MMST; otherwise the shortcut is not taken. The resulting test sequence is called T s. The test sequence T s is fault simulated and all the detected transition faults are dropped. To detect the yetundetected faults the procedure described in the next section is used for extending T s. 5. FAULT-ORIENTED TEST SELECTION We extend the sequence T s into a sequence T s by including tests for the transition faults not detected by T s. Let F r be the set of remaining transition faults. The extension has two parts. In the first part we determine the minimum value of WSA needed to detect the transition faults in F r that are detectable by using tests in T c. We also order these detectable transition faults. In the second part of this phase we extend T s to detect all the detectable transition faults in F r. 5. Determination of detectable transition faults and minimum WSA We know that for every transition fault detected there is a corresponding stuck-at fault that is detected. We determine the set of stuck-at faults called F s corresponding to the transition faults in F r. We fault simulate without fault dropping the stuck-at faults in F s using the tests in T c. During the fault simulation process, for each stuck-at-α fault f in F s we determine the set of tests in T c that detect the fault f as well as the set of tests that set the faulty line to α. These sets of tests in T c correspond to the tests that can detect the corresponding transition fault and initialize the fault, respectively. If the set of initializing tests or the set of detection tests for some transition fault in F r is empty, then the fault is not detectable using the tests in the given T c. Undetectable transition faults in F r are dropped. Knowing the set of tests in T c that can initialize a transition fault f and the set of tests in T c that can detect f, we also know the set of two-pattern tests formed out of tests in T c that detect f. Thus for each transition fault f in F r, we can determine from G s the minimum WSA, denoted by mwsa f, needed to detect the fault. Then the minimum WSA needed to detect all the detectable transition faults, denoted by WSA min, is: WSA min = max(w, max (mwsa f )), f where W is the maximum WSA of an edge in the MMST found in Phase. For each detectable transition fault f, we determine a level of difficulty which is equal to the minimum of the number of tests in T c that initialize the fault and the number of tests in T c that detect the fault. We then order the faults in F r in ascending order of their level of difficulty. Let the ordered set of detectable transition faults be F r. In the next step described below we extend the test sequence T s obtained after Phase to detect the faults in F r. We consider the faults in F r in order. 5.2 Extending T s We extend T s in three ways to detect faults in F r. These are illustrated in Figure 4. In Figure 4(a) a sequence T s with tests from T c is given. This sequence yields three twopattern tests <t, t 2 >, <t 2, t 3 >, <t 3, t 4 >. This sequence can be extended in three different ways depicted in Figure 4(b) through 4(d). The extended sequence of Figure 4(b) gives one additional two-pattern test <t 4, t 5 >, whereas the extended sequences of Figure 4(c) and Figure 4(d) give two additional two-pattern tests. The sequence of Figure 4(c) gives additional tests <t 4, t 5 > and <t 5, t 6 >, and the sequence of Figure 4(d) gives additional tests <t 2, t 5 > and <t 5, t 2 >. 507

5 t t2 t3 t4 (a) t t2 t3 t4 t5 (b) t t2 t3 t4 t5 (c) t t2 t3 t4 t5 (d) Figure 4. Methods to extend T s In extending T s into a test sequence T s we pick a yetundetected transition fault, say f, at the top of the ordered set of faults F r and then extend the current test sequence by one or two nodes as illustrated in Figure 4 such that the resulting two-pattern tests detect f and none of the twopattern tests added by this extension require WSA greater than WSA min determined in the first part of this phase. We fault simulate the two-pattern tests added by the extensions and remove all the detected faults from F r. We repeat the extension step until all the faults in F r are detected. The final test sequence obtained is called T s. An extension of T s to detect all the faults in F r always exists for the following reason. Consider an arbitrary fault in F r that can be detected by a two-pattern test <t i, t j >. Since t i exists in T s, and since WSA is the same for <t i, t j > and <t j, t i >, the extension of Figure 4(d) can be used to add <t i, t j > to T s and detect the fault. 6. COMPACTION After the fault-oriented test selection described above, the test sequence obtained guarantees the detection of all the detectable faults with a minimum peak WSA. As is well known, test sequences can be compacted further in a postprocessing step. We use forward-looking fault simulation [3] to compact the test sequence. Compared to reverseorder fault simulation, forward-looking simulation can often achieve a larger reduction of test set size with a reduced run time. For transition fault tests which are given as a sequence of tests, we have to make sure the resulting sequence would not violate the peak power constraint of WSA min before we drop any test from the sequence during test compaction. Next we discuss the procedure we use to compact T s. Let T s be {t, t 2,, t n } where every t i, i n, is an element from the test set T c. Mark all the test vectors from t to t n as UNUSED. Conduct forward-looking transition fault simulation on pairs {<t, t 2 >, <t 2, t 3 >,, <t n-, t n >}. If any pair does not detect any new fault or should be skipped without simulation (a feature of forward-looking fault simulation [3]), continue with the next test. Otherwise, mark both vectors in the pair as USED. t6 Scan the test sequence {t, t 2,, t n } from the start vector t. For every UNUSED segment (a segment such that all its vectors are UNUSED): (a) If the UNUSED segment is at the start or the end of T s, remove it. (b) If the UNUSED segment is between two USED vectors t i and t j and if WSA(t i, t j ) is no greater than WSA min, remove the entire segment. Otherwise try to replace the UNUSED segment with an element t k from T c such that both WSA(t i, t k ) and WSA(t k, t j ) are less than or equal to WSA min. If the entire UNUSED segment cannot be replaced by a test t k, shorten the UNUSED segment by marking its last element as USED and try to remove the shortened UNUSED segment or replace it with a single element of T c. Repeat the last step as necessary to determine if a subsequence of the UNUSED segment can be deleted. 7. EXPERIMENTAL RESULTS We implemented the scheme described above in C and experimented with ISCAS89 benchmark circuits. The experiments were run on a Linux machine with a 400 MHz Intel Pentium IV processor and 52MB memory. The stuck-at fault test set we used can detect all the irredundant stuck-at faults [9]. We reproduced the procedure in [6] for comparison. For a fair comparison, we made the following two changes in this reproduced procedure. i) We use forward-looking fault simulation in place of reverse order fault simulation used in [6] since forward-looking fault simulation gives higher compaction. ii) We apply forward-looking fault simulation using all the test vectors instead of just the vectors from the faultoriented phase (i.e., Phase 2) as done in [6]. This gives shorter test sequences. Experimental results are given in Table. After the circuit name, we give the number of tests in T c and the number of transition faults (the set of transition faults is denoted by F tr ). Next, we give the results obtained by the method in [6] including the number of transition fault tests in T s and the number of transition faults detected. The scheme in [6] uses an arbitrary order to visit tests in T c in the first phase and thus may result in different peak WSA values depending on the order. For this reason, we conducted experiments using ten different random orders and recorded both the average peak WSA and maximum peak WSA from these ten experiments. These are reported in the next two columns of Table. The run time of the procedure from [6] is given next. The experimental data obtained by using the proposed method are reported in Table next. The first two columns under the proposed method are similar to those for the method of [6]. Next the peak WSA and percentage reduction in WSA compared to the average peak WSA and the maximum peak WSA for the method of [6] is given. Finally, the run time is given. 508

6 From Table, it can be seen that the proposed method achieves the same transition fault coverage as [6] with reduced peak power dissipation. Compared to the peak WSA in [6], the proposed method reduces the peak WSA by 9% on the average. The run time for the proposed method is higher. The number of tests for the proposed method is similar to the number of tests for the method of [6]. 8. CONCLUSION In this work, we proposed a new low power transition fault ATPG scheme for designs with enhanced scan based on reusing stuck-at fault tests. The peak power requirement of the proposed method is minimum under the constraint of i) a given stuck-at fault test set and ii) uncompromised transition fault coverage. Experimental results showed that the proposed scheme achieves the same transition fault coverage while reducing the peak power by 9% on the average compared to an earlier method. 9. REFERENCES [] J. A. Waicukauski, E. Lindbloom, B. K. Rosen and V. S. Iyengar, Transition Fault Simulation, IEEE Design & Test of Computers, Vol. 4, No. 2, April 987. [2] A. K. Pramanick and S. M. Reddy, On the Detection of Delay Faults, Proc. ITC, pp , Sept. 988 [3] G. L. Smith, Model for Delay Faults Based Upon Paths, Proc. ITC, pp , Sept. 985 [4] C. J. Lin and S. M. Reddy, On Delay Fault Testing in Logic Circuits, IEEE TCAD, pp , Sept. 985 [5] I. Pomeranz and S. M. Reddy, Static Compaction for Two- Pattern Test Sets, Proc. ATS, pp , 995 [6] X. Liu, M. S. Hsiao, S. Chakravarty and P. J. Thadikaran, Novel ATPG Algorithms for Transition Faults, Proc. ETW, pp , May 2002 [7] H. J. Wunderlich and Y. Zorian, Built-In Self Test (BIST) Synthesis of Self-Testable Systems, Kluwer Academic Publisher, 997. [8] Y. Zorian, A Distributed BIST Control Scheme for Complex VLSI Devices, Proc. VTS, pp. 4-9, 993 [9] J. Saxena, et. al., A Case Study of IR-Drop in Structured At- Speed Testing, Proc. ITC, pp [0] V. Dabholkar, S. Chakravarty, I. Pomeranz and S. M. Reddy, Techniques for Minimizing Power Dissipation in Scan and Combinational Circuits During Test Application, IEEE TCAD, pp , 998 [] S. Gerstendorfer and H. J. Wunderlich, Minimized Power Consumption for Scan-based BIST, Proc. ITC, pp , 999. [2] I. Pomeranz and S.M. Reddy, On n-detection Test Sets and Variable n-detection Test Sets for Transition Faults, IEEE TCAD, March 2000, pp [3] I. Pomeranz and S. M. Reddy, Forward-Looking Fault Simulation for Improved Static Compaction, IEEE TCAD, pp , 200 [4] J. Savir and S. Patil, On Broad-Side Delay Test, Proc. VTS, pp , Sept. 994 [5] J. Savir and S. Patil, Scan-Based Transition Test, IEEE TCAD, pp , August 993 [6] B. Dervisoglu and G. Stong, Design for Testability: Using Scanpath Techniques for Path-Delay Test and Measurement, Proc. ITC, pp , 99 [7] T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, MIT Press and McGraw-Hill Book Company, 6th edition, 992 [8] W. Cook, W. H. Cunningham, W. Pulleyblank and A. Schrijver, Combinatorial Optimization, John Wiley & Sons, 998 [9] S. Kajihara, I. Pomeranz, K. Kinoshita and S. M. Reddy, Cost-Effective Generation of Minimum Test Sets for Stuck-at Faults in Combinational Logic Circuits, IEEE TCAD, pp , Dec Table Experimental Results Size of T c &F tr The method in [6] The proposed method T c F tr T s tr_det avg peak max peak time (s) T s tr_det peak avg% max% time (s) s s s s s s Avg